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Using panel data, the fixed effect regression specification is given by

$y_{it} = a_i + \beta' x_{it} + \epsilon_{it}$

where $a_i$ are the fixed effects.

The fixed effects estimator $\beta_{FE}$ eliminates the fixed effects by time-demeaning, i.e.

$\bar{y_i} = \hat{\beta'}_{FE} \bar{x_i} $

where $\bar{y_i} = \sum_{t=1}^T y_{it}/T$ and similarly for $\bar{x_i}$.

The fixed effects can then be recovered by $\hat{\alpha_i} = \bar{y_i} - \hat{\beta'}_{FE} \bar{x_i}$.

My question: How do I get the standard errors for the fixed effects $\hat{\alpha_i}$ without using the least squares dummy variable (LSDV) estimator?

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  • $\begingroup$ Why do you want to estimate $\beta$ without using the LSDV approach? If the standard errors are of interest it seems to me like the LSDV would by far be the easiest way to obtain them, and the two approaches are equivalent. $\endgroup$
    – Phil
    Aug 28, 2019 at 7:42

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